Question

1. solve for x

Explanation:

Step1: Use geometric mean theorem

In a right - triangle, if the altitude is drawn to the hypotenuse, then the geometric mean theorem states that \(x^{2}=4\times(4 + 21)\).

Step2: Calculate the right - hand side

First, calculate \(4+21 = 25\), then \(4\times25=100\). So \(x^{2}=100\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents a length, \(x=\sqrt{100}=10\).

Answer:

10